Backtesting techniques blackare based on quantitative tests which scrutinize model performance in terms of accuracy and blackprecision with respect to a defined criterion.
Existing approaches, however, rely on tests that analyze VaR and ES predictions separately, i.e. they only focus on the individual evaluation of one risk measure or the other.
VaR evaluation is typically based on coverage tests, which measure the percentage of times that the returns have exceeded the estimated VaR at a chosen probability level \(\tau \)  (see, e.g., the unconditional coverage (LR\(_{uc}\) ) test of [1]}, the conditional coverage (LR\(_{cc}\) ) test of [2]} and the Dynamic Quantile (DQ) test of [3]}).
